- #1
member 428835
Hi PF!
I am wondering why we define velocity for polar coordinates as $$\vec{V} = \nabla \times \frac{\psi(r,z)}{r} \vec{e_\theta}$$ and why we define velocity in spherical coordinates as $$\vec{V} = \nabla \times \frac{\psi(r,\phi)}{r \sin \phi} \vec{e_\theta}$$
The only thing I don't understand is why we divide by ##r## and then ##r \sin \phi## (which are really sort of the same dimension, just the spherical is a projection). Is this simply to make the equations that follow nicer?
I am wondering why we define velocity for polar coordinates as $$\vec{V} = \nabla \times \frac{\psi(r,z)}{r} \vec{e_\theta}$$ and why we define velocity in spherical coordinates as $$\vec{V} = \nabla \times \frac{\psi(r,\phi)}{r \sin \phi} \vec{e_\theta}$$
The only thing I don't understand is why we divide by ##r## and then ##r \sin \phi## (which are really sort of the same dimension, just the spherical is a projection). Is this simply to make the equations that follow nicer?